A380720 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2 * (1 - x*A(x))^4) / (1 - x*A(x))^2.

1, 3, 27, 427, 9829, 299421, 11399767, 522120299, 27993612745, 1721382881401, 119487832998811, 9244561661068647, 788985451618181869, 73644131873399817653, 7463589265871298367711, 816231439143125763495811, 95811879190166378655829393, 12015708296507465444922873585

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(3*n-3*k+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(3*n-3*k+1, n-k)/k!);

Crossrefs

Cf. A377742, A380674.

Sequence in context: A377693 A094577 A221624 * A108525 A379699 A136719

Adjacent sequences: A380717 A380718 A380719 * A380721 A380722 A380723

Keyword

nonn

Author

Seiichi Manyama, Jan 30 2025

Status

approved